Random Graphs and Networks: A First Course

by Alan Frieze, Michal Karonski

Overview

Networks surround us, from social networks to protein–protein interaction networks within the cells of our bodies. The theory of random graphs provides a necessary framework for understanding their structure and development. This text provides an accessible introduction to this rapidly expanding subject. It covers all the basic features of random graphs – component structure, matchings and Hamilton cycles, connectivity and chromatic number – before discussing models of real-world networks, including intersection graphs, preferential attachment graphs and small-world models. Based on the authors' own teaching experience, it can be used as a textbook for a one-semester course on random graphs and networks at advanced undergraduate or graduate level. The text includes numerous exercises, with a particular focus on developing students' skills in asymptotic analysis. More challenging problems are accompanied by hints or suggestions for further reading.

Product Details

ISBN-13:	9781009260305
Publisher:	Cambridge University Press
Publication date:	03/09/2023
Pages:	232
Product dimensions:	6.69(w) x 9.61(h) x 0.47(d)

About the Author

Alan Frieze is Professor in the Department of Mathematical Sciences at Carnegie Mellon University. He has authored almost 400 publications in top journals and was a plenary speaker at the 2014 International Congress of Mathematicians.

Michał Karoński is Professor Emeritus in the Faculty of Mathematics and Computer Science at Adam Mickiewicz University, where he founded the Discrete Mathematics group. He served as Editor-in-Chief of 'Random Structures and Algorithms' for thirty years.

Table of Contents

Conventions/Notation; Part I. Preliminaries: 1. Introduction; 2. Basic tools; Part II. Erdos–Rényi–Gilbert Model: 3. Uniform and binomial random graphs; 4. Evolution; 5. Vertex degrees; 6. Connectivity; 7. Small subgraphs; 8. Large subgraphs; 9. Extreme characteristics; Part III. Modeling Complex Networks: 10. Inhomogeneous graphs; 11. Small world; 12. Network processes; 13. Intersection graphs; 14. Weighted graphs; References; Author index; Main index.

Editorial Reviews

‘Random Graphs and Networks: A First Course’ is a wonderful textbook that covers a remarkable set of topics written by two leading experts in the field. The textbook is comprehensive and contains a wealth of theoretical preliminaries, exercises and problems, making it ideal for an introductory course or for self-study. It is the best starting point in the present textbook market for any university student interested in the foundations of network science.’ Charalampos E. Tsourakakis, Boston University

'This is a very concise, highly informative introduction to the theory of random graphs and networks ... Essential.' M. Bona, Choice

From the Publisher